When generalizing the \(n_{\mathbf {k}}\)  to arbitrary dimensions, we need to make certain assumptions on the parameters involved. The contact coefficient \(C_J\)  thus far explored in nuclear system using different theoretical approaches, or in ultra-cold gases adopting different types of trapped potentials, at zero or finite temperatures all show good universality [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, e.g., see Chap. 18 of Ref. [16]} for a review. In this work, we thus assume that the \(C_J\)  (including its \(C_0\)  and \(C_1\)  terms) is also (near) universal with respect to dimension \(d\) . On the other hand, to our best knowledge, there is no fundamental constraints on the high momentum cutoffs in lower or higher dimensions (different from 3). We thus assume that they are also universal and investigate the kinetic EOS of ANM based on these assumptions. Although the SRC-induced HMT appears only in the kinetic EOS (through the single-nucleon momentum distribution function) in the study here, it should be thought as an effective nucleon-nucleon interaction. Here we focus on its effects on the kinetic EOS of ANM in \(d\) D via the \(\epsilon \) -expansion.
